Scaling depth-induced wave-breaking in two-dimensional spectral wave models

• Simple and complex parametric wave breaking scalings provide similar results.
• Wave directionality affects depth-induced wave breaking.
• Scaling with local bottom slope and normalized wave number improves 1D performance.
• 2D performance is improved with both a joint scaling and directional partitioning.

Wave breaking in shallow water is still poorly understood and needs to be better parameterized in 2D spectral wave models. Significant wave heights over horizontal bathymetries are typically under-predicted in locally generated wave conditions and over-predicted in non-locally generated conditions. A joint scaling dependent on both local bottom slope and normalized wave number is presented and is shown to resolve these issues. Compared to the 12 wave breaking parameterizations considered in this study, this joint scaling demonstrates significant improvements, up to ∼50% error reduction, over 1D horizontal bathymetries for both locally and non-locally generated waves. In order to account for the inherent differences between uni-directional (1D) and directionally spread (2D) wave conditions, an extension of the wave breaking dissipation models is presented. By including the effects of wave directionality, rms-errors for the significant wave height are reduced for the best performing parameterizations in conditions with strong directional spreading. With this extension, our joint scaling improves modeling skill for significant wave heights over a verification data set of 11 different 1D laboratory bathymetries, 3 shallow lakes and 4 coastal sites. The corresponding averaged normalized rms-error for significant wave height in the 2D cases varied between 8% and 27%. In comparison, using the default setting with a constant scaling, as used in most presently operating 2D spectral wave models, gave equivalent errors between 15% and 38%.